I've just recently begun to watch (and love) anime, so there’s a lot I haven't watched yet. However, out of what I have watched I have a few favourites – and I'll try to limit myself to only a select few.

(In no particular order, except the first one)

1. Clannad & Clannad After Story - The most beautiful, emotionally moving show I have ever seen.
-Code Geass (I was so absorbed by this series until the very end, and then I wanted to rewatch it immidiately)
-Death Note
-Ouran High School Host Club
-Higurashi No Naku Koro Ni / Higurashi No Naku Koro Ni Kai

Lucky Star, Skip Beat!, and Minami-ke get honourable mentions as they all have some very strong points. Of course Dragonball / Dragonball Z also, simply because it was a large aspect of my childhood.

1. Code Geass both seasons. The ending was so epic and sad, a really well done anime series.
2. Tempa Toppa Gurren Lagann. Nuff said.
3. Evangelion: You Can (Not) Advance. Wow. Just... wow. The animation movie was so well animated and so 'new' despite being ripped off twelve episodes of the actual series. This is a must-see.
4. Noein... it's hard to explain. I'm surprised no one actually wrote a recommendation here for it. I might try it later on.
5. Shakugan no Shana holds a special place in my heart , it was what got me hooked onto anime.

Really? The first one got me intrigued with it's dark mood and the suspense it kept in some parts. The combat scene was a bit shallow, but I thought the part where Shiki jumped off the building and landed on the other one leaving water splashing in her wake the single most visually impressive thing for that movie.
I liked them all xD, I thought 5 was a bit confusing though, since it jumped scene to scene without warning.
Anyways, Kara no Kyoukai made my top 5 anime list lol, WATCH IT PPL!

I don't think I've seen enough anime to make a 'favourites' list. So here's all the anime I've watched, all of which I liked.

Deathnote

Evangelion

Fullmetal Alchemist

Fullmetal Alchemist: Brotherhood

Naruto (Shippuden)

Bleach

One Piece

I saw most of 07-Ghost, but I found it quite boring.

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Blasphemy! I can't see why people like this anime so much, personally I found it mediocre at best, and really boring towards the end. Sure, it might be "deep", but that doesn't justify the lame budget ending.